Can reanalysis have anthropogenic climate trends without model forcing?

This paper shows analytically that a reanalysis made with a frozen model can detect the warming trend due to an increase of greenhouse gases within the atmosphere at its full strength (at least 95% level) after a short transient (less than 100 analysis cycles). The analytical proof is obtained by taking into consideration the following three possible deficiencies in the model used to create first-guess fields: (i) the physical processes responsible for the observed trend (e.g., an increase of greenhouse gases) are completely absent from the model, (ii) the first-guess fields are affected by an initial drift caused by the imbalance between the model equilibrium and the analysis that contains trends due to the observations, and (iii) the model used in the reanalysis has a constant model bias. The imbalance contributes to a systematic reduction in the reanalysis trend compared to the observations. The analytic derivation herein shows that this systematic reduction can be very small (less than 5%) when the observations are available for twice-daily assimilation. Moreover, the frequent analysis cycle is essential to compensate for the impact due to relatively poor space coverage of the observational network, which effectively yields smaller weights assigned to observations in a global data assimilation system. Other major issues about using reanalysis for a long-term trend analysis, particularly the impact of the major changes in the global observing system that took place in the 1950s and in 1979, are not addressed. Here it is merely proven mathematically that using a frozen model in a reanalysis does not cause significant harm to the fidelity of the long-term trend in the reanalysis.